Combining p-values from various statistical methods for microbiome data

Motivation: In the field of microbiome analysis, there exist various statistical methods that have been developed for identifying differentially expressed features, that account for the overdispersion and the high sparsity of microbiome data. However, due to the differences in statistical models or test formulations, it is quite often to have inconsistent significance results across statistical methods, that makes it difficult to determine the importance of microbiome taxa. Thus, it is practically important to have the integration of the result from all statistical methods to determine the importance of microbiome taxa. A standard meta-analysis is a powerful tool for integrative analysis and it provides a summary measure by combining p-values from various statistical methods. While there are many meta-analyses available, it is not easy to choose the best meta-analysis that is the most suitable for microbiome data. Results: In this study, we investigated which meta-analysis method most adequately represents the importance of microbiome taxa. We considered Fisher's method, minimum value of p method, Simes method, Stouffer's method, Kost method, and Cauchy combination test. Through simulation studies, we showed that Cauchy combination test provides the best combined value of p in the sense that it performed the best among the examined methods while controlling the type 1 error rates. Furthermore, it produced high rank similarity with the true ranks. Through the real data application of colorectal cancer microbiome data, we demonstrated that the most highly ranked microbiome taxa by Cauchy combination test have been reported to be associated with colorectal cancer.